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Math Circle: Venn Diagrams and Students of Color

I met recently with half a dozen students of color at Jefferson Elementary, whose teachers had encouraged them to try out the Math Circle class. The idea was for me to lead a demonstration class in which they could meet me and sample the math. Besides the math that we tried out, compass constructions, I also wanted to explain to the students why I was there. Since we’ll be studying sets in the upcoming Math Circle, I decided to explain using the sets of a Venn diagram.

I began by asking the students to fill in the blank: “All of us [the students] are _________, but Mr. Ducharme is not ___________.” After a few more obvious answers, a student gave the answer I was looking for: “We’re all brown and black and yellow and different colors, and you’re not!” I introduced the term “people of color.”

I then put a 2’x3’ piece of paper before the students and asked them to grab about 150 little plastic bears I had borrowed from kindergarten, to represent all the third, fourth, and fifth graders at the school. They had nostalgic memories of playing with the bears in kindergarten, but I warned them that this lesson would go from being funny and fun to surprisingly serious. I drew the first circle of the Venn diagram, and asked them to divide the bears into two groups: students of color and not students of color (i.e., white students.) They came up with about 110 students of color and about 40 white students. I asked Ms. Reed, one of their teachers who was working with us, to correct their division. The correct answer is just about the complement of what the students had: over two-thirds to three-fourths of the students are white, only a minority are students of color. I introduced the term “bias” and we discussed possible reasons that their answers were so biased.

The students were already starting to get quiet, and now serious as I added the second intersecting circle: students who are strong enough to do Math Circle vs. students who are not. I defined the the terms, we went over the possible sets, now four of them, and again I asked the students to distribute the tokens accurately. This is their answer before Ms. Reed made a few smaller corrections.

Finally I added the third circle, students who would actually sign up for Math Circle class at Jefferson vs. those who would not sign up. We reviewed the eight resultant sets, I asked students to distribute the tokens one more time, and we discussed their answers. Then I told them, “I don’t know for sure what will happen here, I can’t predict the future, but I can tell you the past, what has happened in fact in my last three Math Circle classes at three different schools.” Using numbers instead of tokens and only looking at the set of student who signed up for class — for I won’t guess about students I didn’t teach — this is the sobering result.

The optimistic students had placed about six tokens for the intersection of {students of color + strong enough to do Math Circle + actually sign up}, for their school alone. The reality, as of my last three schools, was nearly zero. That, as I explained, was why I had volunteered to come for an hour to introduce myself and Math Circle to them.

We discussed these results and then moved on to more innocent math of compass and straightedge constructions. When I left, four of the students, who appear strong enough to do challenging math, wanted very much to sign up for Math Circle.

Addendum, four months later: Those four did sign up and stayed with it, as did thirteen others to make a class of seventeen. We had majority girls and about half students of color. It was a great class.